If your screen doesn't look like the one below after swiping down in the center of the Home screen when the iPad is unlocked, could you post a screenshot?
Search with iPad
Swipe down from the middle of the Home Screen.
Tap the search field, then enter what you’re looking for.
Do any of the following:
Hide the keyboard and see more results on the screen: Tap Go.
Open a suggested app: Tap it.
Get more information about a search suggestion: Tap it, then tap one of the results to open it.
There's a touch to it so that you're not pulling down the notification center. Try swiping a little below the top edge of the screen instead of at the very top. This may take a little practice.